Question

Identify the value of p.

p = 11
p = 10
p = 12
p = 13

Answer 1

12

Explanation:

5^2 + p^2 = (p+1)^2

25 + p^2 = p^2 + 2p + 1

25 = 2p + 1

24 = 2p

12 = p

Answer 2

(c) p = 12

Explanation:

You may recall that (5, 12, 13) is a Pythagorean triple. That would tell you ...

p = 12

__

If you have not memorized a few useful Pythagorean triples, you can use the Pythagorean theorem to solve for p. The sum of squares of the sides is the square of the hypotenuse:

5² +p² = (p+1)²

p² +25 = p² +2p +1

24 = 2p . . . . . . . . subtract p²+1 from both sides

p = 12 . . . . . . divide by 2

_____

Additional comment

Some of the Pythagorean triples commonly seen in algebra and geometry problems are ...

(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)

Of course, multiples of these are used, too. For example, (6, 8. 10) is a multiple of the (3, 4, 5) triple.